Poissonian Pair Correlation for Bernoulli Orbits

Let \(α, β\in \mathbb{T} = \mathbb{R}/\mathbb{Z}\), and let \((ξ_n)_{n \ge 1}\) be independent random variables taking the values \(α\) and \(β\) with equal probability. We study the random walk \[X_n = ξ_1 + \cdots + ξ_n \pmod 1\] and present a deterministic Diophantine condition on \((α, β)\) that